/*
 * Copyright (c) 2011-2012 Alexander Dubu
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * o  Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
 *
 * o  Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 *
 * o  Neither the name Axil nor the names of its contributors may be used to
 *    endorse or promote products derived from this software without specific
 *    prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */
package axil.stdlib.statistics.function;

import axil.stdlib.numbers.type.Int;
import axil.stdlib.numbers.type.Num;

import java.util.ArrayList;


/**
 * Compute the statistical variance across a collection of numeric values.
 */
public class Variance extends ComplexListCalculation {
    /**
     * Execute the specific statistical function against the given arguments.
     */
    protected Num calculate(ArrayList<Num> values) {
        final int size = values.size();
        final Int sizeN = Int.from(size);
        if (size == 0) {
            return Int.zero;
        }
        /*
         * Variance = Mean of the squares - Square of the mean
         */
        Num sumValues = Int.zero;
        Num sumSquares = Int.zero;
        for (Num nextNum : values)
        {
            sumValues = (Num)sumValues.add(nextNum);
            sumSquares = (Num)sumSquares.add(nextNum.multiply(nextNum));
        }
        Num meanSS = sumSquares.divide(sizeN);
        Num mean = sumValues.divide(sizeN);
        Num squareMean = mean.multiply(mean);
        return (Num)(meanSS).subtract(squareMean);
    }
}
